A survey on the theory of bonds

Li, Zijia; Schicho, Josef; Schröcker, Hans-Peter

doi:10.1093/imamci/dnw048

Cited by 3 publications

(2 citation statements)

References 16 publications

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“…It was proven in [LSS18] that the mobility of a specific joint in a linkage is equivalent to the existence of a bond attached to that joint. Hence, for a mobile linkage, there is always some β for which A β is non-empty.…”

Section: Bond Theorymentioning

confidence: 99%

Classification of Higher Mobility Linkages

Guerreiro¹,

Li²,

Schicho³

2021

Preprint

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Section: Bond Theorymentioning

confidence: 99%

Classification of Higher Mobility Linkages

Guerreiro¹,

Li²,

Schicho³

2021

Preprint

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“…The main technique we use takes inspiration from bond theory, which has been developed to study paradoxical motions of serial manipulators, for example 5R closed chains with two degrees of freedom, or mobile 6R closed chains (see [HSS13,HLSS15,LSS18]). The core idea is to consider a compactification of the space of configurations of a manipulator which admits some nice algebraic properties.…”

Section: Introductionmentioning

confidence: 99%

On the existence of paradoxical motions of generically rigid graphs on the sphere

Gallet,

Grasegger,

Legerský

et al. 2019

Preprint

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We interpret realizations of a graph on the sphere up to rotations as elements of a moduli space of curves of genus zero. We focus on those graphs that admit an assignment of edge lengths on the sphere resulting in a flexible object. Our interpretation of realizations allows us to provide a combinatorial characterization of these graphs in terms of the existence of particular colorings of the edges. Moreover, we determine necessary relations for flexibility between the spherical lengths of the edges. We conclude by classifying all possible motions on the sphere of the complete bipartite graph with 3 + 3 vertices where no two vertices coincide or are antipodal.

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Overconstrained Mechanisms Derived From RPRP Loops

Hsu

Ting

2018

Journal of Mechanical Design

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This paper addresses the assembly strategy capable of deriving a family of overconstrained mechanisms systematically. The modular approach is proposed. It treats the topological synthesis of overconstrained mechanisms as a systematical derivation rather than a random search. The result indicates that a family of overconstrained mechanisms can be constructed by combining legitimate modules. A spatial four-bar linkage containing two revolute joints (R) and two prismatic joints (P) is selected as the source-module for the purpose of demonstration. All mechanisms discovered in this paper were modeled and animated with computer-aided design (CAD) software and their mobility were validated with input–output equations as well as computer simulations. The assembly strategy can serve as a self-contained library of overconstrained mechanisms.

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A survey on the theory of bonds

Cited by 3 publications

References 16 publications

Classification of Higher Mobility Linkages

Classification of Higher Mobility Linkages

On the existence of paradoxical motions of generically rigid graphs on the sphere

Overconstrained Mechanisms Derived From RPRP Loops

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